{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一.E步：确定隐变量，写出Q函数\n",
    "利用朴素贝叶斯进行聚类，显然可以使用我们之前介绍过的EM算法咯...,我们可以假设观测数据$X_i(i=1,2,...,M)$是这样产生的，首先按照概率$\\alpha_k(k=1,2,...,K)$选择第$k$个朴素贝叶斯模型，然后依第$k$个模型的概率分布生成观测数据$X_i$，这个选择的过程可以用隐变量$Z$来表示：   \n",
    "\n",
    "$$\n",
    "Z_{i,k}=\\left\\{\\begin{matrix}\n",
    "1 & 第i个观测来自第k个NB模型\\\\ \n",
    "0 & 否则\n",
    "\\end{matrix}\\right.,i=1,2,...,M,k=1,2,...,K\n",
    "$$  \n",
    "\n",
    "按照$Q$函数所需，我们将它的另外两项写出来：   \n",
    "第一项：全数据的似然函数   \n",
    "\n",
    "$$\n",
    "P(X_i,Z_{i,k}=1\\mid \\theta)=\\alpha_k\\prod_{j=1}^Np_k(X_i^j)\n",
    "$$  \n",
    "\n",
    "这里，$N$表示特征维度,$X_i^j$表示第$i$个观测数据的第$j$维特征取值，$p_k(X_i^j)$表示第$k$个朴素贝叶斯模型的条件概率，$\\theta=\\{\\alpha_k,p_k(X_i^j)\\}$  \n",
    "\n",
    "第二项：隐变量的概率分布   \n",
    "\n",
    "$$\n",
    "P(Z_{i,k}=1\\mid X_i,\\theta^t)=\\frac{\\alpha_k^t\\prod_{j=1}^Np_k(X_i^j)^t}{\\sum_{l=1}^K\\alpha_l^t\\prod_{j=1}^Np_l(X_i^j)^t}=w_{i,k}^t\n",
    "$$    \n",
    "\n",
    "ps：注意有这样一个性质$\\sum_{k=1}^Kw_{i,k}^t=1$\n",
    "\n",
    "所以，我们的$Q$函数就可以写出来勒：   \n",
    "\n",
    "$$\n",
    "Q(\\theta \\mid \\theta^t)=\\sum_{Z_{i,k}}logP(X_i,Z_{i,k}=1\\mid \\theta)\\cdot P(Z_{i,k}=1\\mid X_i,\\theta^t)\\\\\n",
    "=\\sum_{i=1}^M\\sum_{k=1}^Kw_{i,k}^t[log\\alpha_k+\\sum_{j=1}^Nlogp_k(X_i^j)]\\\\\n",
    "=\\sum_{i=1}^M\\sum_{k=1}^Kw_{i,k}^tlog\\alpha_k+\\sum_{k=1}^K\\sum_{i=1}^Mw_{i,k}^t\\sum_{j=1}^N\\sum_{l=1}^{S(j)}logp_k(X_i^j)^{I(X_i^j=f_{j,l})}\\\\\n",
    "s.t. \\sum_{k=1}^K\\alpha_k=1\\\\\n",
    "\\sum_{l=1}^{S(j)} p_k(X_i^j=f_{j,l})=1\n",
    "$$\n",
    "\n",
    "这里，$f_{j,1},f_{j,2},...,f_{j,S(j)}$表示$X_i^j,i=1,2,...,M$中不同取值的集合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二.M步：极大化Q函数\n",
    "$\\alpha_k$与$p_k(X_i^j)$相互没有关联，我们可以将$Q$函数拆解为两个目标函数的极大化过程，由于均含有约束条件，所以需要转换为拉格朗日函数，通过求KKT条件的方式来求解；   \n",
    "\n",
    "#### 求$\\alpha_k^{t+1}$\n",
    "\n",
    "我们可以为$\\alpha_k$构建一个拉格朗日函数：   \n",
    "\n",
    "$$\n",
    "L(\\alpha,\\beta)=-\\sum_{i=1}^M\\sum_{k=1}^Kw_{i,k}^tlog\\alpha_k+\\beta(1-\\sum_{k=1}^K\\alpha_k),\\alpha=\\{\\alpha_1,\\alpha_2,...,\\alpha_K\\}\n",
    "$$  \n",
    "\n",
    "原问题等价于求解：   \n",
    "\n",
    "$$\n",
    "\\alpha^*=\\arg\\min_{\\alpha}\\max_{\\beta}L(\\alpha,\\beta)\n",
    "$$  \n",
    "\n",
    "直接求下KKT条件：   \n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{matrix}\n",
    "\\frac{\\partial L(\\alpha,\\beta)}{\\partial \\alpha_k}=\\frac{-\\sum_{i=1}^Mw_{i,k}^t}{\\alpha_k}-\\beta=0 & k=1,2,...,K\\\\ \n",
    "1-\\sum_{k=1}^K\\alpha_k=0 & \n",
    "\\end{matrix}\\right.\n",
    "\\Rightarrow\\alpha_k^{t+1}=\\frac{\\sum_{i=1}^Mw_{i,k}^t}{M}\n",
    "$$\n",
    "\n",
    "\n",
    "#### 求$p_k(X_i^j)^{t+1}$\n",
    "\n",
    "同样的，我们可以为$p_k(X_i^j)$构建一个拉格朗日函数   \n",
    "\n",
    "$$\n",
    "L(p,\\beta)=-\\sum_{k=1}^K\\sum_{i=1}^Mw_{i,k}^t\\sum_{j=1}^N\\sum_{l=1}^{S(j)}logp_k(X_i^j)^{I(X_i^j=f_{j,l})}+\\sum_{k=1}^K\\sum_{j=1}^N\\beta_{k,j}(1-\\sum_{l=1}^{S(j)} p_k(X_i^j=f_{j,l}))\n",
    "$$\n",
    "\n",
    "原问题等价于：   \n",
    "\n",
    "$$\n",
    "p^*=arg\\min_p\\max_\\beta L(p,\\beta)\n",
    "$$   \n",
    "\n",
    "同样，对其求KKT条件：   \n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{matrix}\n",
    "\\frac{\\partial L(p,\\beta)}{\\partial p_k(X_i^j=f_{j,l})} =-\\frac{\\sum_{i=1}^Mw_{i,k}^t}{p_k(X_i^j=f_{j,l})}-\\beta_{k,j}=0&k=1,2,...,K,j=1,2,...,N \\\\ \n",
    "1-\\sum_{l=1}^{S(j)}p_k(X_i^j=f_{j,l}) & k=1,2,...,K,j=1,2,...,N\n",
    "\\end{matrix}\\right.\\\\\n",
    "\\Rightarrow p_k(X_i^j=f_{j,l})^{t+1}=\\frac{\\sum_{i=1}^Mw_{i,k}^tI(X_i^j=f_{i,l})}{\\sum_{i=1}^Mw_{i,k}^t}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 三.代码实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('../')\n",
    "import numpy as np\n",
    "from ml_models import utils\n",
    "from ml_models.wrapper_models import DataBinWrapper\n",
    "%matplotlib inline\n",
    "\n",
    "\"\"\"\n",
    "使用EM算法进行NB聚类，封装到ml_models.pgm\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "class NaiveBayesCluster(object):\n",
    "    def __init__(self, n_components=1, tol=1e-5, n_iter=100, max_bins=10, verbose=False):\n",
    "        \"\"\"\n",
    "        :param n_components: 朴素贝叶斯模型数量\n",
    "        :param tol: log likehold增益<tol时，停止训练\n",
    "        :param n_iter: 最多迭代次数\n",
    "        :param verbose: 是否可视化训练过程\n",
    "        \"\"\"\n",
    "        self.n_components = n_components\n",
    "        self.tol = tol\n",
    "        self.n_iter = n_iter\n",
    "        self.verbose = verbose\n",
    "        # 分箱\n",
    "        self.dbw = DataBinWrapper(max_bins=max_bins)\n",
    "        # 参数\n",
    "        self.p_y = {}\n",
    "        self.p_x_y = {}\n",
    "        # 默认参数\n",
    "        self.default_y_prob = None  # y的默认概率\n",
    "        self.default_x_prob = {}  # x的默认概率\n",
    "\n",
    "    def get_log_w(self, x_bins):\n",
    "        \"\"\"\n",
    "        获取隐变量\n",
    "        :param x_bins:\n",
    "        :return:\n",
    "        \"\"\"\n",
    "        W = []\n",
    "        for x_row in x_bins:\n",
    "            tmp = []\n",
    "            for k in range(0, self.n_components):\n",
    "                llh = self.p_y[k]\n",
    "                for j, x_ij in enumerate(x_row):\n",
    "                    llh += self.p_x_y[k][j][x_ij]\n",
    "                tmp.append(llh)\n",
    "            W.append(tmp)\n",
    "        W = np.asarray(W)\n",
    "        return W\n",
    "\n",
    "    def fit(self, x):\n",
    "        n_sample = x.shape[0]\n",
    "        self.dbw.fit(x)\n",
    "        x_bins = self.dbw.transform(x)\n",
    "        # 初始化模型参数\n",
    "        self.default_y_prob = np.log(0.5 / self.n_components)  # 默认p_y\n",
    "        for y_label in range(0, self.n_components):\n",
    "            self.p_x_y[y_label] = {}\n",
    "            self.p_y[y_label] = np.log(1.0 / self.n_components)  # 初始p_y设置一样\n",
    "            self.default_x_prob[y_label] = np.log(0.5 / n_sample)  # 默认p_x_y\n",
    "            # 初始p_x_y设置一样\n",
    "            for j in range(0, x_bins.shape[1]):\n",
    "                self.p_x_y[y_label][j] = {}\n",
    "                x_j_set = set(x_bins[:, j])\n",
    "                for x_j in x_j_set:\n",
    "                    # 随机抽样计算条件概率\n",
    "                    sample_x_index = np.random.choice(n_sample, n_sample // self.n_components)\n",
    "                    sample_x_bins = x_bins[sample_x_index]\n",
    "                    p_x_y = (np.sum(sample_x_bins[:, j] == x_j) + 1) / (\n",
    "                        sample_x_bins.shape[0] + len(x_j_set))\n",
    "                    self.p_x_y[y_label][j][x_j] = np.log(p_x_y)\n",
    "        # 计算隐变量\n",
    "        W_log = self.get_log_w(x_bins)\n",
    "        W = utils.softmax(W_log)\n",
    "        W_gen = np.exp(W_log)\n",
    "        current_log_loss = np.log(W_gen.sum(axis=1)).sum()\n",
    "        # 迭代训练\n",
    "        current_epoch = 0\n",
    "        for _ in range(0, self.n_iter):\n",
    "            if self.verbose is True:\n",
    "                utils.plot_decision_function(x, self.predict(x), self)\n",
    "                utils.plt.pause(0.1)\n",
    "                utils.plt.clf()\n",
    "            # 更新模型参数\n",
    "            for k in range(0, self.n_components):\n",
    "                self.p_y[k] = np.log(np.sum(W[:, k]) / n_sample)\n",
    "                for j in range(0, x_bins.shape[1]):\n",
    "                    x_j_set = set(x_bins[:, j])\n",
    "                    for x_j in x_j_set:\n",
    "                        self.p_x_y[k][j][x_j] = np.log(\n",
    "                            1e-10 + np.sum(W[:, k] * (x_bins[:, j] == x_j)) / np.sum(W[:, k]))\n",
    "\n",
    "            # 更新隐变量\n",
    "            W_log = self.get_log_w(x_bins)\n",
    "            W = utils.softmax(W_log)\n",
    "            W_gen = np.exp(W_log)\n",
    "            # 计算log like hold\n",
    "            new_log_loss = np.log(W_gen.sum(axis=1)).sum()\n",
    "            if new_log_loss - current_log_loss > self.tol:\n",
    "                current_log_loss = new_log_loss\n",
    "                current_epoch += 1\n",
    "            else:\n",
    "                print('total epochs:', current_epoch)\n",
    "                break\n",
    "        if self.verbose:\n",
    "            utils.plot_decision_function(x, self.predict(x), self)\n",
    "            utils.plt.show()\n",
    "\n",
    "    def predict_proba(self, x):\n",
    "        x_bins = self.dbw.transform(x)\n",
    "        rst = []\n",
    "        for x_row in x_bins:\n",
    "            tmp = []\n",
    "            for y_index in range(0, self.n_components):\n",
    "                try:\n",
    "                    p_y_log = self.p_y[y_index]\n",
    "                except:\n",
    "                    p_y_log = self.default_y_prob\n",
    "                for i, xij in enumerate(x_row):\n",
    "                    try:\n",
    "                        p_y_log += self.p_x_y[y_index][i][xij]\n",
    "                    except:\n",
    "                        p_y_log += self.default_x_prob[y_index]\n",
    "                tmp.append(p_y_log)\n",
    "            rst.append(tmp)\n",
    "        return utils.softmax(np.asarray(rst))\n",
    "\n",
    "    def predict(self, x):\n",
    "        return np.argmax(self.predict_proba(x), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#造伪数据\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y = make_blobs(n_samples=400, centers=4, cluster_std=0.85, random_state=0)\n",
    "X = X[:, ::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total epochs: 319\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f2dc249198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#查看效果\n",
    "nbc = NaiveBayesCluster(n_iter=500, tol=1e-5, n_components=4, max_bins=20, verbose=False)\n",
    "nbc.fit(X)\n",
    "utils.plot_decision_function(X, y, nbc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现最上面的两种类别基本可以正确圈出来出来，最下面两种类别混为一种了，个人觉得下面两种数据点在横向上概率密度差不多，导致胶着，具体原因还有待探索"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 四.gaussian实现\n",
    "按照前面的套路，我们可以假设$p_k(X_i^j)$来源于某一一维高斯分布$N(x\\mid u_{k,j},\\sigma_{k,j})$，即：   \n",
    "\n",
    "$$\n",
    "p_k(X_i^j)=\\frac{1}{\\sqrt{2\\pi}\\sigma_{k,j}}exp(-\\frac{(X_i^j-u_{k,j})^2}{2\\sigma_{k,j}^2})\n",
    "$$  \n",
    "\n",
    "同样的，可以通过极大似然估计得到均值和标准差的更新公式：   \n",
    "\n",
    "$$\n",
    "u_k^{t+1}=\\frac{\\sum_{i=1}^Mw_{i,k}^tx_i}{\\sum_{i=1}^Mw_{i,k}^t}\\\\\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_{k,j}^{t+1}=\\sqrt{\\frac{\\sum_{i=1}^Mw_{i,k}^t(x_i-u_{k,j}^t)^2}{\\sum_{i=1}^Mw_{i,k}^t}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "使用EM算法进行GaussianNB聚类，封装到ml_models.pgm\n",
    "\"\"\"\n",
    "\n",
    "class GaussianNBCluster(object):\n",
    "    def __init__(self, n_components=1, tol=1e-5, n_iter=100, verbose=False):\n",
    "        \"\"\"\n",
    "        :param n_components: 朴素贝叶斯模型数量\n",
    "        :param tol: log likehold增益<tol时，停止训练\n",
    "        :param n_iter: 最多迭代次数\n",
    "        :param verbose: 是否可视化训练过程\n",
    "        \"\"\"\n",
    "        self.n_components = n_components\n",
    "        self.tol = tol\n",
    "        self.n_iter = n_iter\n",
    "        self.verbose = verbose\n",
    "\n",
    "        # 参数\n",
    "        self.p_y = {}\n",
    "        self.p_x_y = {}\n",
    "        # 默认参数\n",
    "        self.default_y_prob = None  # y的默认概率\n",
    "\n",
    "    def get_w(self, x):\n",
    "        \"\"\"\n",
    "        获取隐变量\n",
    "        :return:\n",
    "        \"\"\"\n",
    "        W = []\n",
    "        for k in range(0, self.n_components):\n",
    "            tmp = []\n",
    "            for j in range(0, x.shape[1]):\n",
    "                tmp.append(np.log(utils.gaussian_1d(x[:, j], self.p_x_y[k][j][0], self.p_x_y[k][j][1])))\n",
    "            W.append(np.sum(tmp, axis=0) + np.log(self.p_y[k]))\n",
    "        W = np.asarray(W)\n",
    "        return np.exp(W.T)\n",
    "\n",
    "    def fit(self, x):\n",
    "        n_sample = x.shape[0]\n",
    "\n",
    "        # 初始化模型参数\n",
    "        self.default_y_prob = np.log(0.5 / self.n_components)  # 默认p_y\n",
    "        for y_label in range(0, self.n_components):\n",
    "            self.p_x_y[y_label] = {}\n",
    "            self.p_y[y_label] = 1.0 / self.n_components  # 初始p_y设置一样\n",
    "            # 初始p_x_y设置一样\n",
    "            for j in range(0, x.shape[1]):\n",
    "                self.p_x_y[y_label][j] = {}\n",
    "                u = np.mean(x[:, j], axis=0) + np.random.random() * (x[:, j].max() + x[:, j].min()) / 2\n",
    "                sigma = np.std(x[:, j])\n",
    "                self.p_x_y[y_label][j] = [u, sigma]\n",
    "\n",
    "        # 计算隐变量\n",
    "        W= self.get_w(x)\n",
    "        current_log_loss = np.log(W.sum(axis=1)).sum()\n",
    "        W = W / np.sum(W, axis=1, keepdims=True)\n",
    "        # 迭代训练\n",
    "        current_epoch = 0\n",
    "        for _ in range(0, self.n_iter):\n",
    "            if self.verbose is True:\n",
    "                utils.plot_decision_function(x, self.predict(x), self)\n",
    "                utils.plt.pause(0.1)\n",
    "                utils.plt.clf()\n",
    "            # 更新模型参数\n",
    "            for k in range(0, self.n_components):\n",
    "                self.p_y[k] = np.sum(W[:, k]) / n_sample\n",
    "                for j in range(0, x.shape[1]):\n",
    "                    x_j = x[:, j]\n",
    "                    u = np.sum(x_j * W[:, k]) / np.sum(W[:, k])\n",
    "                    sigma = np.sqrt(np.sum((x_j - u) * (x_j - u) * W[:, k]) / np.sum(W[:, k]))\n",
    "                    self.p_x_y[k][j] = [u, sigma]\n",
    "\n",
    "            # 更新隐变量\n",
    "            W = self.get_w(x)\n",
    "            new_log_loss = np.log(W.sum(axis=1)).sum()\n",
    "            W = W / np.sum(W, axis=1, keepdims=True)\n",
    "            if new_log_loss - current_log_loss > self.tol:\n",
    "                current_log_loss = new_log_loss\n",
    "                current_epoch += 1\n",
    "            else:\n",
    "                print('total epochs:', current_epoch)\n",
    "                break\n",
    "        if self.verbose:\n",
    "            utils.plot_decision_function(x, self.predict(x), self)\n",
    "            utils.plt.show()\n",
    "\n",
    "    def predict_proba(self, x):\n",
    "        rst = []\n",
    "        for x_row in x:\n",
    "            tmp = []\n",
    "            for y_index in range(0, self.n_components):\n",
    "                try:\n",
    "                    p_y_log = self.p_y[y_index]\n",
    "                except:\n",
    "                    p_y_log = self.default_y_prob\n",
    "                for i, xij in enumerate(x_row):\n",
    "                    p_y_log += np.log(\n",
    "                        1e-12 + utils.gaussian_1d(xij, self.p_x_y[y_index][i][0], self.p_x_y[y_index][i][1]))\n",
    "                tmp.append(p_y_log)\n",
    "            rst.append(tmp)\n",
    "        return utils.softmax(np.asarray(rst))\n",
    "\n",
    "    def predict(self, x):\n",
    "        return np.argmax(self.predict_proba(x), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total epochs: 59\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f2df17f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#查看效果\n",
    "gnb = GaussianNBCluster(n_iter=200, tol=1e-5, n_components=4,verbose=False)\n",
    "gnb.fit(X)\n",
    "utils.plot_decision_function(X, y, gnb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
